How to only show preview for template_ID_preview?
There is a difference between "ID" properties and other runtime ones.
An ID property has the basic structure for Blender to save it in the file.
Materials, textures, etc, are IDs (they are part of the .blend file), the HDR previews from that add-on are not (they are in a directory in the disk, and previewed in Blender, but they are not saved in a .blend, unless you actually load one into a texture which is then saved).

Firstly, you should understand if you are presenting ID or non-ID properties. If they are just temporary properties, template_icon_view should be used instead of template_ID_preview.

If you really want ID properties, then the selector comes with some more features for management of the data that is saved (rename, unlink, see the users). At the moment this is not optional, except the '+' to make a new one.
If you want just a preview with no management options, but also with no selector, there istemplate_preview. The buttons on the side are optional.

The template_icon_view was introduced along with the matcaps for Blender 2.66, but the ability to have custom previews from files is from 2.75. https://wiki.blender.org/index.php/User:Brita/Proposals/UIPreviews